Debt contracts in the presence of performance manipulation

Abstract

Empirical evidence suggests that firms often manipulate reported numbers to avoid debt covenant violations. We study how a firm’s ability to manipulate reports affects the terms of its debt contracts and the resulting investment and manipulation decisions that the firm implements. Our model generates novel empirical predictions regarding the use and the level of debt covenant, the interest rate, the efficiency of investment decisions, and the likelihood of covenant violations. For example, the model predicts that the optimal debt contract for firms with relatively strong (weak) corporate governance (i.e., cost of manipulation) induces overinvestment (underinvestment). Moreover, for firms with strong (weak) corporate governance, an increase in corporate governance quality leads to tighter (looser) covenant, more (less) frequent covenant violations and lower (higher) interest rate. Our model highlights that the interest rate, which is a common proxy for the cost of debt, neither accounts for the distortion of investment efficiency nor the expected manipulation costs arising under debt financing. We propose a measure of cost of debt capital that accounts for these effects.

would have at least three solutions, which is a contradiction. Hence, the function \(\mathcal {K}\left (\tau \right ) \) has a unique minimum over the interval \(\left [ 0,\hat {\tau }\right ] \), denoted \(\tau ^{+}\), given by

Suppose \(\tau ^{\ast }>K\). This implies that the lender’s expected payoff from continuation, given \(\tau ^{\ast }\), is strictly greater than his payoff upon termination, which is L. That is

$$E\left( \min \left\{ x,K\right\} |s=\tau^{\ast }\right) >I>L. $$

Therefore, the lender strictly prefers to continue the project when \(s=\tau ^{\ast }\). The manager always prefers to continue the project. This implies there is a feasible contract that offers the lender the same face value and a lower threshold, and does not induce higher expected manipulation cost. Such a contract Pareto dominates the assumed contract; hence, a contract with \(\tau ^{\ast }>K^{\ast }\) is suboptimal. □

Proof of Lemma 2

We need to show that in any equilibrium \(\mathcal {K}^{\prime }\left (\tau \right ) \leq 0\). Let \(\left \{ z^{\ast },K^{\ast }\right \} \) be the equilibrium threshold and face value, then the manager’s expected payoff can be written as

When \(\tau ^{\ast }\leq K\) a manager with a signal \(s=\tau ^{\ast }\) obtains positive expected payoff only if the signal is wrong, in which case his payoff from continuation is independent of \(\tau ^{\ast }\). This implies that \(z^{\ast }-\tau ^{\ast }\) is independent of \(\tau ^{\ast }\). In such a case, offering the contract \(\left \{ z^{o},K^{\ast }\right \} \) is preferable to the lender, increases the likelihood of continuation (which is beneficial to the manager), and will have no effect on the manager’s expected manipulation cost. As such, the contract \(\left \{ z^{o},K^{\ast }\right \} \) is feasible and strictly dominates the contract \(\left \{ z^{\ast },K^{\ast }\right \} \) for which \(\mathcal {K}^{\prime }\left (\tau ^{\ast }\right ) >0\).

Finally, Lemma 3 proves that \(z^{\ast }=h\rightarrow \frac { dz^{\ast }}{dc}<0,\) so there is only one value \(\tilde {c}\) such that \( z^{\ast }=h,\) and \(z^{\ast }<h\) if and only if \(c>\tilde {c}\). Now, when \( z^{\ast }=h,\) the optimal threshold satisfies

By assumption \(V^{FB}>\mathbb {E}\left (x\right ) \). We argue that for \(\rho \) high enough, the debt contract includes a covenant, even as \(c\rightarrow 0\). Suppose we implement τFB as the contract’s threshold (perhaps sub-optimally) and set the face value accordingly at \(\mathcal {K}\left (\tau ^{FB}\right ) \) to satisfy the lender’s participation constraint. Assuming the contract leads to \(z\left (\tau ^{FB}\right ) >h\) (which we can always guarantee by making c small enough), then the expected payoff of the manager is

This means we can select \(\rho \ \)close to 1, denoted \(\rho ^{+}\), to ensure

$${\Pi} \left( \tau^{FB}|\rho^{+}\right) +I>E(x)\text{.} $$

Of course, for a fixed \(c,\) a large \(\rho \) may lead to \(\zeta \left (\tau ^{FB}\right ) <h\). So to ensure \(\zeta \left (\tau ^{FB}\right ) >h,\) we pick \( c\) small enough, say \(c_{0}\), such that

\(\hat {\rho }\) is the precision level such that the firm is indifferent between using a covenant and not using one. Next we argue that the firm will use a covenant if and only if \(\rho \geq \hat {\rho }\). Suppose, by contradiction, that for some \(\rho \in \left (\hat {\rho },1\right ) \) the firm does not use a covenant. Then we have that

Hence, the contract we have constructed yields both higher continuation cash flows and lower misreporting costs under \(\rho \) than the optimal debt contract under \(\hat {\rho }\), hence it must dominate a no-covenant contract. To prove the other direction suppose \(\rho <\hat {\rho },\) but the debt contract includes a covenant, so

which is a contradiction. Next, we show that when \(\rho \geq \hat {\rho }\) there is over-continuation if and only if the cost of misreporting is higher than \(\hat {c}\). Define \(\tau ^{\ast }\left (c\right ) \) as

such that if \(c\leq \hat {c}\) (resp. \(c>\hat {c}\)) there is over-termination (resp. over-continuation).

Consider uniqueness of the optimal threshold \(\tau ^{\ast }\). When \(z^{\ast }\geq h\) the proof follows by contradiction. In this case, the first order condition of \(V^{\prime }(\tau )=\chi ^{\prime }(\tau )\) is a third order polynomial and has at most three real solutions, but the smallest solution is negative. The other two consecutive solutions cannot be both maxima, hence the maximum must be unique. When \(z^{\ast }<h\) the first order condition is a fourth order polynomial, so there can be (at most) two local maxima of \({\Pi } \left (\tau \right ) \) . Now, we will show that one of the maxima lies on \([\frac {h}{1-\rho },\infty ),\) being outside the relevant range. Indeed,

(Note that \(\tau ^{\ast }\left (c\right ) \) is not necessarily the optimal threshold since the optimal debt contract may use no covenant, in which case \(z^{\ast }=\tau ^{\ast }= 0\).)

Lemma 3 proves there is a unique value of \(c,\) denoted \(\tilde { c},\) such that the covenant is \(z^{\ast }=h\). If \(c<\tilde {c}\) (resp. \(c> \tilde {c}\)) the covenant is larger (smaller) than h. On the other hand,

Beyer, A. (2013). Conservatism and aggregation: The effect on cost of equity capital and the efficiency of debt contracts. Rock Center for Corporate Governance at Stanford University Working Paper, (120).Google Scholar